We assume that the input vectors \(x_1,\dots , x_n \in ^d\)  and the weights \(\lambda _1,\dots , \lambda _n\)  have polynomially bounded entries (i.e., every number lies \([-(nd), (nd)]\)  and is specified by \(O(\log (nd))\)  bits). The only infinite-precision numbers are the \(p\) -stable random variables and the exponential random variables, so we will discretize them so they require only \(O(\log (nd))\)  random bits to generate them. Similarly to Claim 3 of [1]} our algorithm's output, as a function of the \(p\) -stable and exponential random variables, always considers polynomially bounded entries and has bounded derivatives in all but a \(1/(nd)\) -fraction of the probability space. With probability \(1 / (nd)\) , the \(p\) -stable random variables may become too large or exponentials too small. Furthermore, for any fixed setting of the \(p\) -stable random variables, a discontinuity in the algorithm's output occurs when the exponential random variables cause \(\)  may suddenly switch, when the maximum of \(_k\)  in (REF ) is not unique. When we discretize the exponential distribution, the probability this occurs is at most \(1/(nd)\) .
